Mathematics of NMR Shielding¶
This section works through the theory behind the NMR shielding calculation covered in How NMR Calculation Works, in more mathematical detail.
- The Nuclear Magnetic Shielding Tensor, how shielding is defined as a second derivative of the energy.
- The Gauge Origin Problem, why the choice of gauge origin matters, and where it goes wrong with finite basis sets.
- Gauge-Including Atomic Orbitals (GIAO), how GIAO fixes the gauge origin problem.
- Coupled-Perturbed Equations for Shielding, solving for the field-dependent response of the wavefunction.
- Isotropic Shielding and Anisotropy, extracting physically meaningful numbers from the shielding tensor.
- Referencing Chemical Shifts, converting an absolute shielding constant into an experimentally comparable chemical shift.